Invariant Speed of Light using Binary Stars and Tangential Velocity So I was in class the other day and my professor mentioned that we can prove that light is invariant using a binary star system.
His reasoning:


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*Assume a binary star system 1000-light years away from Earth, with the stars orbiting counterclockwise.

*Assume stars rotating at 0.003c and stars positions at top and bottom of orbit. The time light takes to get from top star to earth is longer than the bottom star.
My question is how does this show that light is invariant?

 A: Assuming we have a way to determine the time it takes light to reach us, this gives us a way to validate one of two hypotheses. Either:


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*The speed of light is not invariant, which means its speed is dependent on the source velocity, or

*The speed of light is invariant, which means its speed is independent of the source velocity.
Under hypothesis 1, the light coming from one star is traveling faster than the other (since the two stars have different velocities relative to Earth), and under hypothesis 2, the light coming from each star has the same speed. Since the stars are the same distance away, under hypothesis 1, the faster light should reach us first, and under hypothesis 2, the light from both stars should reach us at the same time.
Experimentally, we have determined that hypothesis 2 is correct.
A: Binary system are quoted as a way to check the velocity of the star does not affect the speed of propagation of light, but, as far as I know the argument uses the amount of light observed at earth.
If the velocity of the rotating stars does not affect the speed of light we should observe the same amount of light no matter the phase of the orbital motion of the stars. 
